Overview

Binary Tree Package

Abstract

This package provides Binary- RedBlack- and AVL-Trees written in Python and Cython/C.

This Classes are much slower than the built-in dict class, but all iterators/generators yielding data in sorted key order. Trees can be uses as drop in replacement for dicts in most cases.

Source of Algorithms

AVL- and RBTree algorithms taken from Julienne Walker: http://eternallyconfuzzled.com/jsw_home.aspx

Trees written in Python

  • BinaryTree -- unbalanced binary tree
  • AVLTree -- balanced AVL-Tree
  • RBTree -- balanced Red-Black-Tree

Trees written with C-Functions and Cython as wrapper

  • FastBinaryTree -- unbalanced binary tree
  • FastAVLTree -- balanced AVL-Tree
  • FastRBTree -- balanced Red-Black-Tree

All trees provides the same API, the pickle protocol is supported.

Cython-Trees have C-structs as tree-nodes and C-functions for low level operations:

  • insert
  • remove
  • get_value
  • min_item
  • max_item
  • prev_item
  • succ_item
  • floor_item
  • ceiling_item

Constructor

  • Tree() -> new empty tree;
  • Tree(mapping) -> new tree initialized from a mapping (requires only an items() method)
  • Tree(seq) -> new tree initialized from seq [(k1, v1), (k2, v2), ... (kn, vn)]

Methods

  • __contains__(k) -> True if T has a key k, else False, O(log(n))
  • __delitem__(y) <==> del T[y], del[s:e], O(log(n))
  • __getitem__(y) <==> T[y], T[s:e], O(log(n))
  • __iter__() <==> iter(T)
  • __len__() <==> len(T), O(1)
  • __max__() <==> max(T), get max item (k,v) of T, O(log(n))
  • __min__() <==> min(T), get min item (k,v) of T, O(log(n))
  • __and__(other) <==> T & other, intersection
  • __or__(other) <==> T | other, union
  • __sub__(other) <==> T - other, difference
  • __xor__(other) <==> T ^ other, symmetric_difference
  • __repr__() <==> repr(T)
  • __setitem__(k, v) <==> T[k] = v, O(log(n))
  • clear() -> None, remove all items from T, O(n)
  • copy() -> a shallow copy of T, O(n*log(n))
  • discard(k) -> None, remove k from T, if k is present, O(log(n))
  • get(k[,d]) -> T[k] if k in T, else d, O(log(n))
  • is_empty() -> True if len(T) == 0, O(1)
  • items([reverse]) -> generator for (k, v) items of T, O(n)
  • keys([reverse]) -> generator for keys of T, O(n)
  • values([reverse]) -> generator for values of T, O(n)
  • pop(k[,d]) -> v, remove specified key and return the corresponding value, O(log(n))
  • pop_item() -> (k, v), remove and return some (key, value) pair as a 2-tuple, O(log(n)) (synonym popitem() exist)
  • set_default(k[,d]) -> value, T.get(k, d), also set T[k]=d if k not in T, O(log(n)) (synonym setdefault() exist)
  • update(E) -> None. Update T from dict/iterable E, O(E*log(n))
  • foreach(f, [order]) -> visit all nodes of tree (0 = 'inorder', -1 = 'preorder' or +1 = 'postorder') and call f(k, v) for each node, O(n)
  • iter_items(s, e[, reverse]) -> generator for (k, v) items of T for s <= key < e, O(n)
  • remove_items(keys) -> None, remove items by keys, O(n)

slicing by keys

  • item_slice(s, e[, reverse]) -> generator for (k, v) items of T for s <= key < e, O(n), synonym for iter_items(...)
  • key_slice(s, e[, reverse]) -> generator for keys of T for s <= key < e, O(n)
  • value_slice(s, e[, reverse]) -> generator for values of T for s <= key < e, O(n)
  • T[s:e] -> TreeSlice object, with keys in range s <= key < e, O(n)
  • del T[s:e] -> remove items by key slicing, for s <= key < e, O(n)

start/end parameter:

  • if 's' is None or T[:e] TreeSlice/iterator starts with value of min_key();
  • if 'e' is None or T[s:] TreeSlice/iterator ends with value of max_key();
  • T[:] is a TreeSlice which represents the whole tree;

TreeSlice is a tree wrapper with range check and contains no references to objects, deleting objects in the associated tree also deletes the object in the TreeSlice.

  • TreeSlice[k] -> get value for key k, raises KeyError if k not exists in range s:e

  • TreeSlice[s1:e1] -> TreeSlice object, with keys in range s1 <= key < e1
    • new lower bound is max(s, s1)
    • new upper bound is min(e, e1)

TreeSlice methods:

  • items() -> generator for (k, v) items of T, O(n)
  • keys() -> generator for keys of T, O(n)
  • values() -> generator for values of T, O(n)
  • __iter__ <==> keys()
  • __repr__ <==> repr(T)
  • __contains__(key)-> True if TreeSlice has a key k, else False, O(log(n))

prev/succ operations

  • prev_item(key) -> get (k, v) pair, where k is predecessor to key, O(log(n))
  • prev_key(key) -> k, get the predecessor of key, O(log(n))
  • succ_item(key) -> get (k,v) pair as a 2-tuple, where k is successor to key, O(log(n))
  • succ_key(key) -> k, get the successor of key, O(log(n))
  • floor_item(key) -> get (k, v) pair, where k is the greatest key less than or equal to key, O(log(n))
  • floor_key(key) -> k, get the greatest key less than or equal to key, O(log(n))
  • ceiling_item(key) -> get (k, v) pair, where k is the smallest key greater than or equal to key, O(log(n))
  • ceiling_key(key) -> k, get the smallest key greater than or equal to key, O(log(n))

Heap methods

  • max_item() -> get largest (key, value) pair of T, O(log(n))
  • max_key() -> get largest key of T, O(log(n))
  • min_item() -> get smallest (key, value) pair of T, O(log(n))
  • min_key() -> get smallest key of T, O(log(n))
  • pop_min() -> (k, v), remove item with minimum key, O(log(n))
  • pop_max() -> (k, v), remove item with maximum key, O(log(n))
  • nlargest(i[,pop]) -> get list of i largest items (k, v), O(i*log(n))
  • nsmallest(i[,pop]) -> get list of i smallest items (k, v), O(i*log(n))

Set methods (using frozenset)

  • intersection(t1, t2, ...) -> Tree with keys common to all trees
  • union(t1, t2, ...) -> Tree with keys from either trees
  • difference(t1, t2, ...) -> Tree with keys in T but not any of t1, t2, ...
  • symmetric_difference(t1) -> Tree with keys in either T and t1 but not both
  • is_subset(S) -> True if every element in T is in S (synonym issubset() exist)
  • is_superset(S) -> True if every element in S is in T (synonym issuperset() exist)
  • is_disjoint(S) -> True if T has a null intersection with S (synonym isdisjoint() exist)

Classmethods

  • from_keys(S[,v]) -> New tree with keys from S and values equal to v. (synonym fromkeys() exist)

Installation

from source:

python setup.py install

or from PyPI:

pip install bintrees

Compiling the fast Trees requires Cython and on Windows is a C-Compiler necessary (MingW works fine).

Download Binaries for Windows

http://bitbucket.org/mozman/bintrees/downloads

Documentation

this README.rst

bintrees can be found on bitbucket.org at:

http://bitbucket.org/mozman/bintrees